The present invention relates to copying methods and apparatus and, more particularly, to a method and apparatus for correcting for the distortion that results when copying pages of a book pressed against the document support glass of a copying machine or a document scanner.
Ever since the introduction of xerographic photocopiers many users have experienced difficulty in producing clear, non-distorted copies from opened books or volumes that have been pressed upon the flat document glass. This difficulty is mainly due to the fact that conventional photographic copiers are designed to produce copies from documents (generally, single sheets) that lay flat upon the document glass. Textbooks with hard bindings cannot be so oriented.
The crease of a typical textbook generally pyramids upwardly away from the glass, thus causing an upside-down xe2x80x9cV-shapedxe2x80x9d surface. This is especially so for thick books with hard covers. The crease falls outside of the focal length range for which the copier lens can properly project the image of the book onto the image receiving medium or pre-charged paper. In other words, the crease cannot be focused properly to provide an undistorted image. As a result, the copied crease is often blurred, distorted, and darkened.
In order to make the copies more legible, the operator of the copier is required to forcibly press on the backing of the book as it rests upon the glass. Sometimes this will work. However, many times the binding is too stiff and the crease cannot be projected into the fold. pressing with excessive force is also risky, as it may cause damage to the binding. In some cases, an immoderate amount of force may even break the glass.
In the last twenty-five years numerous apparatus have been invented or proposed to solve this problem. Most of them either do not work, or are impractical. A simple one-piece optical corrective or compensation lens was invented to cure these problems and was described in U.S. Pat. No. 6,313,954, granted to the present inventor on Nov. 6, 2001 for CORRECTIVE LENS FOR COPYING BOOKS.
The optical corrective lens of the ""954 patent is basically composed of three parts: a thick curvilinear optical lens in the center, and two very thin extension leaves or arms spread outward from each side of the center lens. The only optically functional part of the lens is the center portion. The main purpose of the extension leaves is to eliminate the glitches in the copies caused by light deflections along the edges of the center lens. The surface contours of the center lens are basically a composition of sections of circular surfaces or circular-like elliptical and parabolic surfaces.
Although the results were not perfect, the lens worked for making duplications from book pages using a commercial xerographic copier. However, it was later revealed that the lens was difficult to manufacture using any of the existing conventional and economical plastic fabrication processes like injection molding, blowing, or continuous extruding. This is due to the extremely thin cross-section of the large extension leaves, which had to be seamlessly fabricated as an integral part of a relatively thick center lens. To improve the lens""s manufacturability, the thickness of the extension leaves must be substantially increased. However, the increase of the extension leaves will also increase the profile of the center lens; otherwise, the radius of each constituent section of the top surface of the center lens must be reduced accordingly. Either way, the optical performance of the lens will be substantially worsened.
Several such lenses were built to fine tune this design for thicker (0.050 inch) extension leaves. The quality of a typical xerographic copy of the pages of a thick reference book produced using a typical xerographic copier with any of these trial lenses is obviously much poorer than the similar copy demonstrated in Tai""s patent application. There are two darkened strips proximate the centerline. Characters close to these darkened strips are over-magnified and darker than the rest of the characters in the copy. Characters in center areas a little bit farther away from the centerline are still somewhat insufficiently decompressed or under-magnified. Copies with such poor quality are unsightly but may still be considered acceptable for reading purposes. However, its application to text scanning and digitizing is questionable due to more stringent decompression requirements.
After a laborious attempt to improve the performance of the lens, it was clear that the types of surfaces proposed and suggested to construct the lens""s most crucial bottom surface are inadequate. Thus, it was found that to make the basic design of this lens work properly, adequate curvature must be found for the constituent sections of the most crucial bottom surface. Without scientific theory or principle available to guide the work, some innovation or breakthrough was needed.
In U.S. Pat. No. 3,609,030, issued to Meyer L. Sugarman et al. on Sep. 28, 1971 for ELECTROSTATIC BOOK COPIER, a tabletop electrostatic book copier is illustrated, having an exposure station on its top. The book to be copied is placed on top of a vertical exposure station and the image of the book is projected directly to the pre-charged paper through a mirror and an optical lens. The image of the book surface is projected using an ordinary optical lens and a mirror found in conventional copiers. The image is projected directly onto a charged paper instead of onto an image-receiving medium. There is no teaching or suggestion of using a distorted lens to refocus the page of the document.
In U.S. Pat. No. 4,585,334, issued to Brian R. Malyon on Apr. 29, 1986 for DOCUMENT COPIERS, a document copier is shown that incorporates a scanner with a forty-five degree slanted scanning window glass mounted at the end of a rectangular housing. The ninety-degree corner, or the so-called wedge, between the window glass and one of the sidewalls points downwardly. The book to be copied is placed on a rack below the scanner window glass. The rack is constructed from two flat frames connected together at a ninety-degree angle, with its opening facing upward. The book to be copied is faced upwardly and rests on the rack with its inside pages opened at a ninety-degree angle. During the copying process, the rack first moves up, bringing the half opened book toward the scanner. It then stops at a predetermined position and keeps a surface of the book page away from the scanner window to prevent damaging the book. In this position, the opposite inside page of the book is under the scanner housing, facing the sidewall. It may or may not touch the slanted sidewall. The scanner then scans the surface of the inside page of the book under its window.
In U.S. Pat. No. 4,763,173, issued to Michael E. Harrigan et al. on Aug. 9, 1988 for IMAGING SYSTEM FOR COMPENSATING FOR IMAGE DISTORTION DUE TO WRINKLED OR CURLED DOCUMENTS, a document imaging system is shown including a positive, aspheric, Fresnel lens. The purpose of the system is to compensate for small, smooth wrinkles and curls of the original document to be copied.
In U.S. Pat. No. 5,071,252, issued to William Howseman, Jr. on Dec. 10, 1991 and Japanese patent No. JP 360,186,360A, issued to Kenich Watabiki, it is suggested that book size bundles of numerous short optical fibers shaped in a nearly flat triangular prism be placed between an opened book and the copier""s document glass to optically bring the images of the book pages to the copier""s document supporting glass. Neither of these inventors addressed the solutions of other related problems such as the illumination of the book page""s surfaces, the solution to the decompression of the text recorded on the book pages, etc. The principles and mechanisms they employed are very different from that used in the invention proposed in this application.
In Japanese patent Number JP 63,254,437A issued to Tatsuya Shimoda on Oct. 21, 1988, the use of an optical apparatus composed of two slightly bent convex lenses connected together by a flexible hinge is suggested for compensating the pyramiding of the book pages adjacent to the book""s binding. In the application, the flat ridge formed by the thin edges and the flexible hinge is proposed to be placed directly under the crease 7 formed by the facing inside book pages and the flat portions of the book pages 4 residing on the thicker center portions of the constituent lenses. Since convex lenses do not project the images of objects to a viewer closer than the lenses"" viewer side surfaces, the optical compensating effect is very limited for portions of book surfaces deep in the crease where the most compensation is needed. In addition, the thick center portions of the lenses under the flat portions of the book pages will adversely raise the entire profile of the book page""s surfaces higher and, thus, the expected optical compensation effect is significantly further reduced. Although this invention also attempts to use convex lenses to compensate the added height of the portions of book pages adjacent the binding, it uses a very different mechanism and the spirit of his design is upon the flexible hinge that connects the edges of two convex lenses. That is very different from the single rigid lens design proposed in the invention described in this application.
In Japanese patent Number JP 55,052,073A issued to Hirosuke Okura on Apr. 16, 1980, a flat prism made of a transparent material is proposed to be used for compensating the added book page surface height in the crease formed adjacent to the binding of a book. prism is well known for its ability to deflect the rays of a light beam when the light beams approach and leave the prism with an angle. It neither has the capability to reposition the image of an object nor of deflecting a light beam when it strikes or leaves the prism perpendicular to any of its flat surfaces. Therefore, it is obvious that this device doesn""t have the capability of repositioning the image of the book pages"" surfaces to help solve the blurring or image compression problem that the invention in this application attempts to solve.
In the aforementioned U.S. Pat. No. 6,313,954, issued to Chgarles C. Tai on Nov. 6, 2001 for CORRECTIVE LENS FOR COPYING BOOKS, a corrective lens for copying books is described that is capable of compensating the pyramiding of the book pages near the book""s binding, although with some imperfections. These imperfections may be tolerable for making readable xerographic copies from books, but they cause severe problems in scanning the contents of books for digitizing purposes using less expensive desktop scanners. Furthermore, the imperfections caused by the use of the suggested cylindrical or cylindrical-like surfaces to construct the lens""s bottom surface are amplified with the thickening of the lens""s extension arms. The requirement of very thin extension leaves makes it difficult to manufacture using existing economical plastic fabricating processes without sacrificing its performance. Thus, the fundamental surface curvature must be redefined to substantially lower the manufacturing cost and benefit users by providing affordable book copying corrective lenses.
In accordance with the present invention, there is provided a substantially flexible, freely movable, and easily manufacturable corrective lens that yields undistorted copies of adjacent book pages presented for xerographic copying or scanning. The corrective lens is substantially large and rectangular in shape to cover various sizes of books. The lens is placed between the spread pages of the book to be copied and the document glass of the copier. The corrective lens has a mid-portion or center section extending into the crease of a typical opened book where it changes the focal point to accommodate the variable height of the text disposed at the inner edge of the pages. The lens extends outwardly from the center section to form substantially flat side portions, which structurally keep the pages of the open book in place during the copying procedure.
In order to assist the users of this lens in producing copies from books, the lens must be able to help them overcome the following four commonly faced problems: the compression of the image of the text, the blurring of the image of the text, the widened and darkened centerline, and the missing information recorded in the crease between facing book pages. To date, there is neither any scientific theory or principles available to do this nor any existing guidelines to point in the direction of the development of such a surface contour. Therefore, an innovative idea or breakthrough is needed.
A particular surface contour governed by a higher-order skewed hyperbolic-like equation was tried with astonishing results. The prototype lenses were built using surfaces with contours based on this equation and with substantially thicker extension leaves. They were tested and proven capable of simultaneously solving all of the aforementioned problems. Hereinafter, in order to simplify the name of this particularly shaped surface, the higher-order skewed hyperbolic-like curvilinear surface is called the curvilinear skewed hyperbolic surface or, simply, the skewed hyperbolic surface. Mathematically, the x- and y-coordinate relationship of a point on the contour of this particular type of curvilinear surface is governed, or can be defined, by the following equation:
(X+Xo)xc3x97(Y+Yo)n=A+f(X,Y)xe2x80x83xe2x80x83(1)
where:
X is the x-directional Cartesian coordinate position of a point on the curve;
Y is the y-directional Cartesian coordinate position of that point on the curve;
Xo is an empirically determined X-positional constant for the curve;
Yo is an empirically determined y-positional constant for the curve;
n is an empirically determined skew power constant having a value between 0.9 and 2.5 for this particular application;
A is an empirically determined x-directional shape factor of the curve; and
f(X,Y) is an empirically determined small second-order correction factor that corrects the curvatures of the surfaces near the tip of the bottom surface as well as the connections between the curved center lens portion and the flat extension arms.
In the actual design, sections of these particularly shaped surfaces are used to construct the most optically crucial bottom surface of the lens.
From an image formation viewpoint, it is preferable to have the lens""s top and bottom surfaces constructed using sections of differently curved skewed-hyperbolic surfaces. However, the lens""s top surface also serves as a mechanism to stop and keep the surfaces of inside pages of the book to be copied at a predetermined position for better image projection. In addition, it is not as optically crucial as the bottom surface for obtaining a sharp and properly decompressed image of the book pages residing on the lens""s top surface. Therefore, similar to the inventor""s previous lens design, the lens""s top surface is composed of surfaces with contours closely resembling the surface contour of the surfaces of inside pages of a typical thick textbook when it is opened and pressed upon a flat surface. The resemblance between the book""s surface and the lens""s top surface assures intimate contact when the book is opened and pressed onto the lens""s top surface.
In order to further improve the performance of this newly developed corrective lens, the top surfaces of this lens are slightly modified. The two halves of the lens""s top surface are slightly pushed further apart outwardly from the center to assure the intimate contact between the lens""s top surface and the surfaces of the book""s inside pages. In addition, the ridge of the lens""s top surface is made slightly higher and sharper to make it capable of opening the crease further for better scanning of the text inside the crease. Furthermore, the portions of top surface near the bottom edges of the lens are slightly modified to smoothen the transitions of the lens""s extension leaves from curved surfaces to flat top surfaces.
The extension arms or leaves of the lens are large, relatively thin, and rectangular in shape with almost constant cross-sections through their full length. They are thin but not substantially thin so as to prevent the lens from being injection molded.
The innovation of using higher-order curvilinear hyper-elliptical surfaces in this invention effectively improves the performance of the simple corrective lens, allowing the lens to help scan and digitize recorded text on inside pages of books. This also allows manufacturability using existing low-cost plastic fabricating processes without losing performance. Thus, the lens can be mass-produced at a substantially low manufacturing cost, benefiting anyone wishing to conduct book copying or scanning. The alternative design proposed in this invention extends its application to books two inches thick or more without substantially sacrificing the quality of the copies.
A lens with symmetrical left-hand and right-hand halves is most suitable for helping make clear copies of pages for most books. However, for making copies of the first and last few pages of a book, a non-symmetrical lens fits better to the non-symmetrical contour of the inside pages of a thick book. Therefore, the lens can be varied to accommodate different top surface contours.
Furthermore, the curvatures of the sloped portions of the inside pages of an opened, thick book are quite different and less curved than those of a thinner book. Therefore, as shown in FIG. 11, the profiles of the center lens portions of the top surfaces must be raised higher to accommodate the less curved surfaces; in other words, deepen the crease of the opened, thick book. As a result, a portion of these surfaces adjacent to the ridge would be raised higher than the maximum height that the lens can compensate. Although the portions of book pages residing on these portions of the lens may be within the binding edge margin and contain no text, the images would still appear blackened due to severe blurring.
In order to erase or white-out these unsightly darkened marks from the copies, one may coat these small portions of the bottom surfaces with opaque paint or cover them with films or thin covers.
In most cases, very thick books are also large in size and cannot fit two full pages within the boundary of the document glass of an ordinary copier. Therefore, a user of this corrective lens can only copy one page at a time. The partial image of the other page is unnecessary and, sometimes even undesirable. Thus, it is suggested in this invention to offset the top surfaces and the bottom surfaces. With one more degree of freedom allowed by this offsetting, the right-hand side of the lens in FIG. 11 can be designed to clearly capture a larger area of the book page or deepen the crease formed by the opposite book pages. On the other hand, this offset will double the width of the blackened area in the image of the left-hand page, normally unnecessary anyway. Similarly, the entire unnecessary side of a partial page image can be optically erased or whited out with paint, film, or a thin cover.
The lens improves the quality of the copies produced from the inside pages of a book simultaneously in five ways:
1) It works as an optical lens to project an image of the book surface closer to the copier""s document support glass than the actual surfaces of the book pages, thus, helping the copier""s lens to better focus and produce a crisp image of the book surface near its binding.
2) It optically stretches or decompresses the book image near its binding. As a result, the images of characters or pictures in this area are stretched back to their original shapes printed on the inside pages of the book.
3) The ridge helps to open up the book near the binding, enabling the images of the characters and pictures in this area to be more clearly scanned by the copier.
4) The top surfaces of the lens work as a guide to help the inside pages easily and smoothly slide outward without being squeezed toward each other.
5) It enables the use of thicker extension leaves to ease the difficulty in manufacturing without scarifying the lens""s performance.
It is an object of this invention to provide improved means of perfecting the performance of the corrective lens of U.S. Pat. No. 6,313,954 and make it capable of helping users conduct text scanning and digitizing from inside pages of thick books or bound volumes.
It is another object of this invention to provide an improved means of making this lens capable of being inexpensively mass-produced using existing conventional plastic fabricating processes without losing valuable performance.
A further object of this invention is to provide improved means for compensating for the distance between the crease of a book and regions proximate thereto, during a photocopying process that does not require complex structural modifications to conventional copying machines.
It is a further object of this invention to provide improved means for the lens to act as a wedge to spread the pages of a book closest to the binding thereof.
It is a further object of this invention to provide an improved freely movable lens for placement between an open book to be copied and the document glass of a copier, wherein the lens changes its local focal point in accordance with the distance between the book page""s surface and the copier""s document glass across the crease.
A further object of this invention is to provide means to alter the lens and make it capable of producing clear, crisp, and distortion-free copies or scanned images from extra thick books.